From their office, cathy drives due west while john drives south. when john is 7 mi from the office, the distance between them is 1 mi more than cathy’s distance from the office. find the distance between cathy and john.

Let x represent the distance between Cathy and John. The geometry of the problem makes that distance be the hypotenuse of a right triangle with legs 7 and (x -1). Then x is the solution to
.. x^2 = (x -1)^2 +7^2 . . . . Pythagorean theorem
.. 0 = -2x +1 +49 . . . . . . . eliminate parentheses and subtract x^2
.. 2x = 50 . . . . . . . . . . . . . simplify and add 2x
.. x = 25 . . . . . . . . . . . . . . divide by 2

The distance between Cathy and John is 25 miles.